With The Boring Company, which he launched earlier this year, Musk intends to dig tunnels that could provide alternative routes for vehicles, potentially alleviating traffic in metropolitan areas. Musk has said the tunnels could also be used by the Hyperloop, his idea for a hypothetical magnetic train that can travel at 700 mph through vacuum-sealed tubes.

The entrepreneur has already begun digging under SpaceX's Los Angeles headquarters, and tweeted last month that he's had "promising conversations" with mayor Eric Garcetti about building a network of tunnels under the city.

It's not clear how serious the verbal approval is at this point, nor who specifically gave it to build the East Coast route. But a handshake deal probably is unlikely to get very far, given the number of governing bodies that would need to sign off on such a project. And The Boring Company digging the tunnels doesn't necessarily mean the rail itself will get built: Estimates have put the cost of the Hyperloop at more than $100 million per mile.

Musk initially proposed the idea for the Hyperloop in 2013, but he hasn't been directly involved with the startups, such as Hyperloop One and Hyperloop Transportation Technologies, that are working to develop it.

Musk's tweet comes at a time when New York City is in the midst of massive transportation issues due to its centuries-old infrastructure. The "Summer of Hell" has become a trending topic on social media in recent weeks, as commuters post photos of platforms overflowing with people and subway passengers riding between subway cars due to lack of room inside. Governor Andrew Cuomo and Mayor Bill de Blasio have come under fire for doing little to address the problems.

Shortly after Musk's tweet, de Blasio's press secretary, Eric Phillips, responded to Musk's announcement with his own tweet suggesting the mayor knows nothing of the verbal approval.

In response to a query from Inc., de Blasio's deputy press secretary, Ben Sarle, said via email, "Nobody in City Hall, or any of our city agencies, has heard from Mr. Musk or any representatives of his company."

Musk then seemed to soften his earlier statement in subsequent tweets:

Still a lot of work needed to receive formal approval, but am optimistic that will occur rapidly